further maths p1

Question 1

cosine rule

Answer 1

a2 = b2 + c2 - 2bccosA

Question 2

second derivative interpretation

Answer 2

if it’s bigger than 0 its a local minimum
if its less than 0 its a local maximum
if its equal to 0 it could be a point of inflection, a minimum or maximum

Question 3

increasing vs decreasing functions

Answer 3

increasing - gradient is always bigger than 0
decreasing - gradient is always less than 0

Question 4

multiple transformations

Answer 4

Matrix B x Matrix A would be written as AB because you go inside out

Question 5

transformation P followed by transformation Q is written as …

Answer 5

QP

Question 6

matrix for reflection in the y axis

Answer 6

-1 0
0 1

Question 7

identity matrix

Answer 7

1 0
0 1

Question 8

reflection in the line y = x

Answer 8

0 1
1 0

Question 9

reflection in the line y = - x

Answer 9

0 -1
-1 0

Question 10

reflection in the x axis

Answer 10

1 0
0 -1

Question 11

rotation 90 clockwise

Answer 11

0 1
-1 0

Question 12

rotation 180

Answer 12

-1 0
0 -1

Question 13

rotation 90 anticlockwise

Answer 13

0 -1
1 0

Question 14

how to add or subtract matrices

Answer 14

if they’re the same dimensions you just add or subtract to the corresponding number

Question 15

compatible matrices

Answer 15

2 by 2 x 2 by 4

(rows then columns)

inside must be the same then the outside is the dimensions of the product matrix

Question 16

sin

Answer 16

sin x = sin 180 - x
repeats every 360

Question 17

cos

Answer 17

cos x = cos 360 - x
repeat every 360

Question 18

tan

Answer 18

tan x = tan x + 180
repeats every 180

Question 19

pascals triangle

Answer 19

the 1 at the top is technically for the power of 0
signs should be alternating

Question 20

equation for circle not at origin

Answer 20

(x - a) 2 + (y - b) 2 = r 2

Question 21

trig identities